The Steps of Carry Arbitrage in Derivatives

All right, so previously we talked about the money and cash flow perspective of carry arbitrage, but what about the order of this arbitrage? I think that's worth considering because you will not live in a textbook scenario. If you have to do this arbitrage, you're going to enter a certain contract, and you're going to follow certain steps. So, let's do that.

First, because it's arbitrage, you have to, you know, not use your own money. So first, it's not about borrowing money, of course, because you need to find this arbitrage opportunity. In order to find this opportunity, you need to enter a contract. For example, you're going to sell a specific underlying asset in the future. Right now, I'm going to use T to represent that future. You just enter this contract at the initialization of these contracts; no transaction actually happens. It's just a legal obligation that you're going to sell something in the future, and other people are going to buy things from you in the future. There are just two people meeting face to face, or they just send some email and some legal contract, and they just sign it. So, there's no actual transaction happening, just a legal obligation.

Once you know that you're going to sell that specific asset at that specific T in the future, you're going to find these assets. Right now, you don't have this asset, so what are you going to do? You're going to buy this asset, but you don't have any money, or if you have money, you don't want to use it. Because we are doing arbitrage, we don't use our money during the arbitrage. So, what are you going to do? Pretty simple, you're going to borrow money. Borrow money maybe from a bank or any other third parties. For simplicity, let's say you borrow from a bank. You're going to buy that specific underlying asset. The asset's price at time zero will be S0, and you can borrow that amount of money. Once you borrow that amount of money, you're going to owe interest because you're going to pay that borrowed money back, but that repayment will happen in the future. It will have a certain interest, which will depend on whether you are compounding or something like that. For simplicity, let's say it's 1 + r at time T; that will be our interest, which will be paid later.

Once you have that amount of money, you can buy the assets, and that asset will be S0. Since this is carry arbitrage, you're going to carry all the way to time T, and you're going to repay the bank S0 + 1 + r compounded to the T interest back. Since you already have these assets at that specific time, you're going to sell these assets at a certain price. That F will be settled in the obligation that's already written in the contract. So, if it's already written, you're going to sell at the exact same price that is written in the contract, and that specific thing will be settled in the contract. That F, that certain price, is already settled at time zero, so it's already written in the contract. You are going to get that amount of money when you sell this underlying asset at F0. This is the amount of money that you will get. At that specific time in the market, there will be a market price of that underlying asset at specific time T. This amount of money will be the money that you are actually making because that will be the contract value. Essentially, you just have a right to sell that specific thing. Since you already set the price to F0 and the market price is ST, the difference will be this contract's value.

So, that's the process of carry arbitrage.